Decked out in green, a colour they had worn just once before at the Stadio Olimpico back in 1954, Roberto Mancini's new-look Azzurri pushed their perfect run in Group J to seven games for a maximum 21 points.
Despite being pegged back by the Greeks for over an hour the Italians confirmed their dominance and are now assured of finishing top of the group.
Chelsea midfielder Jorginho slotted in a penalty after 63 minutes in the Italian capital with Juventus forward Federico Bernardeschi scoring the second goal on 78 minutes.
"I want to thank the fans at the Olimpico for supporting us, even in the first half when we were not brilliant, maybe a little nervous at being back in Rome," said Mancini.